Nuprl Lemma : adjacent-to-same2
∀[T:Type]. ∀[L:T List]. ∀[a,b,c:T].
(b = c ∈ T) supposing (adjacent(T;L;c;a) and adjacent(T;L;b;a) and no_repeats(T;L))
Proof
Definitions occuring in Statement :
adjacent: adjacent(T;L;x;y),
no_repeats: no_repeats(T;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
before-adjacent,
adjacent_wf,
no_repeats_wf,
list_wf,
adjacent-before,
l_before_antisymmetry
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
unionElimination,
voidElimination
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[a,b,c:T].
(b = c) supposing (adjacent(T;L;c;a) and adjacent(T;L;b;a) and no\_repeats(T;L))
Date html generated:
2016_05_15-PM-03_41_55
Last ObjectModification:
2015_12_27-PM-01_18_17
Theory : general
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